Are Quantum States “Real”?

Busy day today, despite it being a Sunday, so I’ve only got time for a quick post, by way of a diversion while I take a break for a cup of tea.

There’s been an attack of the hyperbolics this week arising from a paper entitled “The quantum state cannot be interpreted statistically”. The abstract of the paper reads:

Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics. Here we show that, given only very mild assumptions, the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory. This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology. If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality.

According to a commentary published in the journal Nature, this paper could “rock quantum theory to the core” and a number of quantum physicists have reacted, e.g.:

“I don’t like to sound hyperbolic, but I think the word ‘seismic’ is likely to apply to this paper,” says Antony Valentini, a theoretical physicist specializing in quantum foundations at Clemson University in South Carolina.

I have to admit I haven’t had time to read the paper in detail yet, so I’m just passing this on as something fresh that may be of wider interest, rather than something I’ve got particularly strong views about. I have to admit, though, that I find the way quantum theorists use words, especially what is meant by “physically real” and what “states of reality” could be. Can a mathematical theorem ever prove itself to be applicable to the physical world anyway? You’ll see that ontology was never my strong suit.

However, if anyone out there in blogland has read this paper and would like to pass on their thoughts for the edification of me and my readers I’d be delighted. I might return to it in a longer post if and when I’ve been able to digest it fully.

When the authors consider the “wavefunction-is-statistical” position, what they mean by it is a certain class of hidden-variable-like theories. They show that those theories give predictions distinct from quantum mechanics and hence are testable. If one happens to think that the theories in question are plausible, then the fact that they’re testable is interesting. If not, not. It’s not clear to me that anybody in the “wavefunction-is-statistical” camp has something like these theories in mind, so I’m not convinced that this result has much bearing on the question.

Agreed. I too need to read it in full, but under those “very mild” assumptions might be things that are more objectionable than the conclusions which the paper reaches. For example causality, which we already know is violated in quanum expts; see quantum blog entries here passim.

They want to make arguments about reality but their model is based on preparing a pure state absolutely isolated from external influences…

I think it is necessary to identify at least three parts of the world (system, observer, environment) before making any nontrivial statement about quantum measurement; in baseball parlance, by this count they don’t even reach first base.

I haven’t read the entire paper, but from what I’ve read and seen summarised, I don’t understand how this is all that new. Just nicely phrased.

We’ve known you can’t interpret the wavefunction purely in statistical terms for a long time, and hidden variables was ruled out by Bell (or Aspect, if you prefer experimental confirmation to theoretical prediction).

Locality was knocked on the head four centuries ago by Isaac Newton, when his successful theory of gravity was posited upon “action at a distance”. There isn’t a falling off with distance in the present case, but the leap to nonlocality is conceptually no different.

I’ve spent an evening looking at Pusey, Barrett, and Rudolph’s paper, and the commentary by Matt Leifer, Scott Aaronson, and David Wallace. The more I think about it, the more I agree with Scott Aaronson when he says, “PBR’s main result reminds me a little of the No-Cloning Theorem: it’s a profound triviality, something that most people who thought about quantum mechanics already knew, but probably didn’t know they knew.” In fact, it may be that many people who think about quantum foundations for a living did already know they knew this; I’m still not totally convinced that the PBR paper says anything that this earlier paper by Brun, Finkelstein, and Mermin doesn’t.

To explain how I’ve come to this way of thinking, I’ll make a tongue-in-cheek statement that isn’t entirely tongue-in-cheek. PBR claim they’re psi-ontologists ruling out a psi-epistemic interpretation of pure quantum states, but I suspect they’re secretly operationalists verifying that quantum mechanics has a certain property which would be desirable in an operational theory.

PBR start off with the assumption that you believe in the standard formalism of quantum mechanics. In particular, they assume you believe that if a system A can be described by the pure state a, and an independent system B can be described by the pure state b, then the composite system consisting of A and B can be described by the pure state a ⊗ b. They conclude that if you try to describe two systems in the same “physical state” λ using two different pure states, and you believe the two pure-state descriptions can be used totally interchangeably, you will make a prediction inconsistent with the predictions of quantum mechanics.

But what is this “physical state” λ? What kind of mathematical object is it? What use is it to an experimentalist like me? PBR are almost totally agnostic about these questions. As far as I can tell, they assume just one thing about λ:

An important assumption for the argument now is that the behaviour of the measuring device—in particular the probabilities for different outcomes—is only determined by the complete physical state of the two systems at the time of measurement, along with the physical properties of the measuring device.

The only thing PBR demand of the “physical state” of a system is that it should completely determine the probability of any outcome of any experiment that could be performed on the system. In other words, the “physical state” is just the complete operational description of a system.

To an operationalist, the meaning of PBR’s result is now transparent. PBR have shown that in quantum mechanics, two systems which are experimentally indistinguishable cannot be described by two different pure states. This is a really nice property for an operational theory to have! It’s such a nice property, in fact, that I find it hard to believe nobody had verified it before. But maybe I’m wrong—there’s a first time for everything, and history has shown that “profound trivialities” in quantum mechanics often go unnoticed far longer than you’d expect.

“The only thing PBR demand of the “physical state” of a system is that it should completely determine the probability of any outcome of any experiment that could be performed on the system.”

Yes, but the probability conditioned on what [whose] information? Some of us fuddy-duddies would like the physical state of a system to completely determine the actual outcome of any experiment that could be performed on the system…